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Edge-matching Puzzle
An edge-matching puzzle is a type of tiling puzzle involving tiling an area with (typically regular) polygons whose edges are distinguished with colours or patterns, in such a way that the edges of adjacent tiles match. Edge-matching puzzles are known to be NP-complete, and capable of conversion to and from equivalent jigsaw puzzles and polyomino packing puzzle. The first edge-matching puzzles were patented in the U.S. by E. L. Thurston in 1892. Current examples of commercial edge-matching puzzles include the Eternity II puzzle, Tantrix, Kadon Enterprises' range of edge-matching puzzles, and the Edge Match Puzzles iPhone app. Notable variations MacMahon Squares MacMahon Squares is the name given to a recreational math puzzle suggested by British mathematician Percy MacMahon, who published a treatise on edge-colouring of a variety of shapes in 1921. This particular puzzle uses 24 tiles consisting of all permutations of 3 colors for the edges of a square. The tiles must be arra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eternity II 2
Eternity, in common parlance, means infinite time that never ends or the quality, condition, or fact of being everlasting or eternal. Classical philosophy, however, defines eternity as what is timeless or exists outside time, whereas sempiternity corresponds to infinite duration. Philosophy Classical philosophy defines eternity as what exists outside time, as in describing timeless supernatural beings and forces, distinguished from sempiternity which corresponds to infinite time, as described in requiem prayers for the dead. Some thinkers, such as Aristotle, suggest the eternity of the natural cosmos in regard to both past and future eternal duration. Boethius defined eternity as "simultaneously full and perfect possession of interminable life". Thomas Aquinas believed that God's eternity does not cease, as it is without either a beginning or an end; the concept of eternity is of divine simplicity, thus incapable of being defined or fully understood by humankind. Thomas H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Art Of Computer Programming
''The Art of Computer Programming'' (''TAOCP'') is a comprehensive monograph written by the computer scientist Donald Knuth presenting programming algorithms and their analysis. Volumes 1–5 are intended to represent the central core of computer programming for sequential machines. When Knuth began the project in 1962, he originally conceived of it as a single book with twelve chapters. The first three volumes of what was then expected to be a seven-volume set were published in 1968, 1969, and 1973. Work began in earnest on Volume 4 in 1973, but was suspended in 1977 for work on typesetting prompted by the second edition of Volume 2. Writing of the final copy of Volume 4A began in longhand in 2001, and the first online pre-fascicle, 2A, appeared later in 2001. The first published installment of Volume 4 appeared in paperback as Fascicle 2 in 2005. The hardback Volume 4A, combining Volume 4, Fascicles 0–4, was published in 2011. Volume 4, Fascicle 6 ("Satisfiability") was rel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carcassonne (board Game)
''Carcassonne'' () is a Tile-based game, tile-based German-style board game for two to five players, designed by Klaus-Jürgen Wrede and published in 2000 by Hans im Glück in German and by Rio Grande Games (until 2012) and Z-Man Games (currently) in English. It received the Spiel des Jahres and the Deutscher Spiele Preis awards in 2001. It is named after the medieval fortified town of Carcassonne in southern France, famed for its city walls. The game has spawned many expansions and spin-offs, and several PC, console and mobile versions. A new edition, with updated artwork on the tiles and the box, was released in 2014. Gameplay The game board is a medieval landscape built by the players as the game progresses. The game starts with a single specific terrain tile face up and 71 others shuffled face down for the players to draw from. Each player's turn consists of three distinct phases: # Draw and place a terrain tile # Station a follower on the newly-placed tile (optional) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regular Polyhedron
A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags. A regular polyhedron is highly symmetrical, being all of edge-transitive, vertex-transitive and face-transitive. In classical contexts, many different equivalent definitions are used; a common one is that the faces are congruent regular polygons which are assembled in the same way around each vertex. A regular polyhedron is identified by its Schläfli symbol of the form , where ''n'' is the number of sides of each face and ''m'' the number of faces meeting at each vertex. There are 5 finite convex regular polyhedra (the Platonic solids), and four regular star polyhedra (the Kepler–Poinsot polyhedra), making nine regular polyhedra in all. In addition, there are five regular compounds of the regular polyhedra. The regular polyhedra There are five convex regular polyhedra, known as the Platonic solids, four regular star polyhedra, the Kepler–Poinsot polyhedra, and five regular compounds ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Space
Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, that is, in Euclid's Elements, Euclid's ''Elements'', it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean spaces of any positive integer dimension (mathematics), dimension, including the three-dimensional space and the ''Euclidean plane'' (dimension two). The qualifier "Euclidean" is used to distinguish Euclidean spaces from other spaces that were later considered in physics and modern mathematics. Ancient History of geometry#Greek geometry, Greek geometers introduced Euclidean space for modeling the physical space. Their work was collected by the Greek mathematics, ancient Greek mathematician Euclid in his ''Elements'', with the great innovation of ''mathematical proof, proving'' all properties of the space as theorems, by starting from a few fundamental properties, called ''postulates'', which either were considered as eviden ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2D Geometric Model
A 2D geometric model is a geometric model of an object as a two-dimensional figure, usually on the Euclidean or Cartesian plane. Even though all material objects are three-dimensional, a 2D geometric model is often adequate for certain flat objects, such as paper cut-outs and machine parts made of sheet metal. Other examples include circles used as a model of thunderstorms, which can be considered flat when viewed from above. 2D geometric models are also convenient for describing certain types of artificial images, such as technical diagrams, logos, the glyphs of a font, etc. They are an essential tool of 2D computer graphics and often used as components of 3D geometric models, e.g. to describe the decals to be applied to a car model. Modern architecture practice "digital rendering" which is a technique used to form a perception of a 2-D geometric model as of a 3-D geometric model designed through descriptive geometry and computerized equipment. 2D geometric modeling techniques ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract Strategy Game
Abstract strategy games admit a number of definitions which distinguish these from strategy games in general, mostly involving no or minimal narrative theme, outcomes determined only by player choice (with no randomness), and perfect information. For example, Go is a pure abstract strategy game since it fulfills all three criteria; chess and related games are nearly so but feature a recognizable theme of ancient warfare; and Stratego is borderline since it is deterministic, loosely based on 19th-century Napoleonic warfare, and features concealed information. Definition Combinatorial games have no randomizers such as dice, no simultaneous movement, nor hidden information. Some games that do have these elements are sometimes classified as abstract strategy games. (Games such as '' Continuo'', Octiles, '' Can't Stop'', and Sequence, could be considered abstract strategy games, despite having a luck or bluffing element.) A smaller category of abstract strategy games manages to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Serpentiles
Serpentiles is the name coined by Kurt N. Van Ness for the hexagonal tiles used in various edge-matching puzzle connection abstract strategy games, such as Psyche-Paths, Kaliko, and Tantrix. For each tile, one to three colors are used to draw paths linking the six sides together in various configurations. Each side is connected to another side by a specific path route and color. Gameplay generally proceeds so that players take turns laying down tiles. During each turn, a tile is laid adjacent to existing tiles so that colored paths are contiguous across tile edges. ''Serpentiles'' is also the name of a single-player puzzle connection game developed by Brett J. Gilbert and published by ThinkFun in 2008. The ''Serpentiles'' (2008) game includes square (1×1) and rectangular (2×1) tiles and challenge cards which provide a list of tiles that should be arranged to make a contiguous path. Tile notation Van Ness also coined a three-digit notation for tile categories, based on the paths s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Serpentile 021 3C 0-GR-B
Serpentiles is the name coined by Kurt N. Van Ness for the hexagonal tiles used in various edge-matching puzzle connection abstract strategy games, such as Psyche-Paths, Kaliko, and Tantrix. For each tile, one to three colors are used to draw paths linking the six sides together in various configurations. Each side is connected to another side by a specific path route and color. Gameplay generally proceeds so that players take turns laying down tiles. During each turn, a tile is laid adjacent to existing tiles so that colored paths are contiguous across tile edges. ''Serpentiles'' is also the name of a single-player puzzle connection game developed by Brett J. Gilbert and published by ThinkFun in 2008. The ''Serpentiles'' (2008) game includes square (1×1) and rectangular (2×1) tiles and challenge cards which provide a list of tiles that should be arranged to make a contiguous path. Tile notation Van Ness also coined a three-digit notation for tile categories, based on the paths s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brailey Sims
Brailey Sims (born 26 October 1947) is an Australian mathematician born and educated in Newcastle, New South Wales. He received his BSc from the University of New South Wales in 1969 and, under the supervision of J. R. Giles, a PhD from the same university in 1972. He was on the faculty of the University of New England (Australia) from 1972 to 1989. In 1990 he took up an appointment at the University of Newcastle (Australia). where he was Head of Mathematics from 1997 to 2000. He is best known for his work in nonlinear analysis and especially metric fixed point theory and its connections with Banach and metric space geometry, and for his efforts to promote and enhance mathematics at the secondary and tertiary level. Publications His most cited publications are: *Mustafa Z, Sims B. A new approach to generalized metric spaces. ''Journal of Nonlinear and convex Analysis''. 2006 Jan 1;7(2):289. According to Google Scholar Google Scholar is a freely accessible web search engine ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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